Influence of Metal Defects on the Mechanical Properties of ABX3 Perovskite-Type Metal-formate Frameworks

Defects are emerging as a key tool for fine-tuning the stimuli-responsive behavior of coordination polymers and metal–organic frameworks. Here, we study the ramifications of defects on the mechanic...


■ INTRODUCTION
Molecular perovskites are dense coordination networks with an ABX 3 perovskite-type structure, where A and/or X is a molecular ion. These compounds include a wealth of compositions such as formates, 1,2 azides, 3,4 thiocyanates, 5,6 dicyanamides, 7,8 dicyanometallates, 9,10 and, conceptually related, Prussian blue analogues, covering phenomena of fundamental and technological relevance. 11, 12 Compared to their inorganic counterparts, molecular perovskites show additional degrees of chemical and structural freedom as enabled by the presence of polyatomic species. 13,14 For instance, the use of polyatomic A-site cations promotes the occurrence of temperature-and pressure-driven phase changes as a result of order−disorder transitions of the molecular A-site cation, opening a variety of functionality to be exploited. 15,16 Looking at ways to fine-tune material properties, the incorporation of defects have proved to be a tremendously successful approach in porous coordination polymers. 17 For example, the archetypical defective metal−organic framework UiO-66 supports both missing linkers and missing clusters, 18,19 which has implications for e.g. the adsorption properties. 20,21 However, good mechanical properties are a prerequisite for a material to be practically useful and hence there is a strong need to elucidate the interplay between defects and the nonambient behavior. 22 Several studies have been focused on this issue, using both experimental and computational techniques, 19,23,24 but further investigation is still required. Concerning molecular perovskites, the incorporation of a large concentration of Schottky-type metal defects has been achieved recently, 25 and its impact on the stimuli-responsive properties is still unknown.
Here, we study the bulk modulus (B 0 ) and volumetric coefficient of thermal expansion (α V ) of the metal-formate framework [C(NH 2 ) 3 ]Mn II (HCOO) 3 and its defective analogue [C(NH 2 ) 3 ]Fe 2/3 III □ 1/3 (HCOO) 3 (□ = vacancy and C(NH 2 ) 3 = guanidinium) using powder X-ray diffraction (PXRD) under variable temperature and pressure. For simplicity, these will be referred to as GuaMn and GuaFe 2/3 □ 1/3 . We note that these quantities also serve as probes of the Gibbs free energy surface through the relationships , such that our results provide qualitative insight into the free energy surface of these materials.

■ METHODS
All chemicals were used as purchased without further purification. The samples were synthesized by previously reported methods. 26,27 A solution of [C(NH 2 ) 3 ] 2 CO 3 (281.5 mg, 1.56 mmol) and HCOOH (182.5 μL, 4.84 mmol) in methanol (5 mL) was added to a methanolic solution of 0.1 M Mn(NO 3 ) 2 or 0.1 M FeCl 3 (5 mL). The reaction mixture was stirred overnight at room temperature prior to isolation by filtration in vacuo and washing with methanol.
Variable-temperature PXRD data of GuaFe 2/3 □ 1/3 were collected using a STOE stadi P with Mo Kα1 radiation and an Oxford diffraction Cryosystem. Variable-pressure PXRD data of both GuaMn and GuaFe 2/3 □ 1/3 were collected using a homebuilt setup at beamline I15 with λ = 0.4246 Å, Diamond Light Source, UK. 28,29 Data analysis was carried out by Pawley refinement as implemented in the software TOPAS. 30,31 The peakshape was modelled by a pseudo-Voigt function and the background by a Chebyshev polynomial. The variable-pressure unit cell lattice parameters were fitted using the second-order Birch− Murnaghan equation of state as implemented in the software EoSfit-GUI. 32−34

■ RESULTS AND DISCUSSION
GuaMn and GuaFe 2/3 □ 1/3 are topologically identical, but differ in the metal occupancy and symmetry. GuaMn crystallizes in the space group Pnna, 26 driven by R-point octahedral tilting (a 0 b − b − in Glazer notation 35,36 ) and the orientational X-point order of the guanidinium cations [ Figure 1a]. 25 Aliovalent substitution of Mn II in GuaMn with Fe III introduces metal vacancies as a charge compensation mechanism, leading to the composition GuaFe 2/3 □ 1/3 [ Figure 1b]. 27 Despite the large vacancy concentration, structural integrity in GuaFe 2/3 □ 1/3 is retained with only a small lattice strain, on account of the strong hydrogen bonds between the guanidinium and the formate moieties. 37 Given the energy penalty associated with nextneighbor vacancy pairs, the vacancies partially order, which reduces the symmetry to the monoclinic space group P2/n11 (≡P12/c1) with α ∼ 89.5°. 27 The nonstandard setting of the monoclinic space group allows for direct comparison of lattice parameters between orthorhombic GuaMn and monoclinic GuaFe 2/3 □ 1/3 . Notably, coordination networks are known to harbor a wealth of defects, yet missing ion defects are still relatively rare. 17,20,38,39 Variable-pressure diffraction was measured up to 0.4 GPa at I15, Diamond Light Source, using equipment dedicated to accurate control of low pressures. 28 The bulk moduli were calculated using EoSFit and compressibilities by linear fits [ Table 1, Figures S1−S4]. 32 The bulk modulus of GuaMn is 20.0(3) GPa, which is in good agreement with the value obtained over a larger pressure range: B 0 = 21.3 GPa. 41 Compared to other formate-based perovskites, this value is slightly lower than for dimethylammonium metal formates (B 0 = 21.3 GPa for M = Mn II and 26.3 GPa for M = Co II ), 16,42,43 but similar to that of [NH 2 NH 3 ]Zn(HCOO) 3 with B 0 = 19 GPa. 44 The defective GuaFe 2/3 □ 1/3 features a lower bulk modulus of 14.3(2) GPa, which is comparable to the behavior of the heterometallic [C 2 H 5 NH 3 ]K 0.5 Al 0.5 (HCOO) 3 . 45 The difference in bulk moduli of GuaMn and defective GuaFe 2/3 □ 1/3 highlights how defects increase the mechanical compliance of the framework. Importantly, the impact of defects even overcompensates influence of ion size, which is known to make molecular perovskites more robust. 40 Both systems show an anisotropic pressure response with K a > K b > K c , where K i is the compressibility of axis i [Table 1, Figure  1d]. To compare the compressibilities of the two systems, the mechanical building unit approach was employed. 46 The lattice parameters for both systems can be recast as Ä and where r ̅ is the average strut length, that is, the metal−metal distance, and θ is the hinging angle, that is, metal−metal−metal angle within the ac plane [ Figure 1c]. 40 Here, θ > 90°. This approach represents a physically meaningful parametrization of   The Journal of Physical Chemistry C pubs.acs.org/JPCC Article the structural changes upon compression, highlighting the behavior of the pseudocubic 3D network. As expected, the strut length r ̅ decreases with pressure, which is accompanied by an increase in the hinging of the framework [ Figure 1e,f]. The behaviors of r ̅ and θ upon compression rationalize the anisotropic compression. As given in eqs 1 and 2, the cell dimensions are linear functions of r ̅ , but with varying dependence on θ. While c is positively correlated with θ, a is negatively correlated and b is independent. Thus, a is the most compliant direction, as both the decrease of r ̅ and the increase of θ upon compression reduce its length. The converse scenario appears for c: the variations of r ̅ and θ operate in tension, which gives a low value of K c . Chemically, the low expansion can be explained by recognizing that the c axis runs along the planes of the incompressible guanidinium cations. 41 In GuaMn, the opposing effects of r ̅ and θ on K c are equal in magnitude and cancel, leading to zero uniaxial compressibility. Further increase of the hinging mechanism may lead to negative linear compressibility. The defects in GuaFe 2/3 □ 1/3 soften r ̅ , as a result of the larger void space, whereas the pressure-induced increase of θ is unchanged. This does not substantially impact the compressibilities of a and c, but K c increases to a nonzero value.
Furthermore, the thermal behavior of GuaFe 2/3 □ 1/3 was investigated in the range 100−300 K by variable-temperature PXRD. The system remains monoclinic down to 220 K, where additional reflections emerge in the diffraction patterns [ Figures  S5 and S6]. Because of the low symmetry and lack of highresolution synchrotron data, the low-temperature phase was not solved and Pawley refinements 30 were only carried out for the ambient phase. The phase transition in defective GuaFe 2/3 □ 1/3 contrasts with the variable-temperature behavior of GuaMn reported by Collings et al., where the system remained in its ambient phase down to 100 K. 40 Hence, the metal defects alter the phase behavior, which may possibly be driven by the enhancement of flexibility by virtue of the larger free space. It is noteworthy that no phase transition was observed in the variable-pressure XRD data, although it is possible that the signal was not sufficiently strong. Further studies into the lowtemperature phase would be of interest.
The volumetric and linear expansivities (α i for axis i) were calculated in the range 300−230 K by PASCal [Table 1, Figure  2]. 47 GuaMn and GuaFe 2/3 □ 1/3 show equal (within error) volumetric coefficients of thermal expansion and both systems are highly anisotropic. Mirroring the pressure behavior, the linear expansivities decrease in the order |α a | > |α b | > |α c | ( Figure  2 and Table 1). Notably, both compounds exhibit negative thermal expansion (NTE) along the c axis. While rare in purely inorganic compounds, NTE is relatively common amongst formate-based perovskites 40,48 and coordination networks in general. 49,50 It appears that the defects play a less important role in the thermal behavior compared to the pressure response, but it should be noted that the investigated temperature range is relatively small.
Defects clearly modify the mechanical properties of GuaFe 2/3 □ 1/3 relative to GuaMn; removing 1/3 of the transition metals reduces the bulk modulus by ∼30%. With the emerging understanding of defect chemistry in MOFs and coordination polymers, there is also growing interest in the role of defects on mechanical properties. It can be misleading to compare results between different systems, as the results are likely dependent on the precise topologies and type of defects. Additionally, solvent content strongly impacts the mechanical response, which may complicate comparisons. 51 However, we note that defects reduce the bulk modulus of UiO-66 up to a critical concentration and certain Prussian blue analogues, in line with the results presented here. 24,52 This likely results from the increased void space, which correlates with greater ease of compression. 53 Comparisons of similar studies may enable the development of general guidelines regarding the influence of defects on the mechanical properties in dense and porous coordination polymers.

■ CONCLUSIONS
To conclude, we report the stimuli-responsive behavior of defect-free [C(NH 2 ) 3 ]Mn II (HCOO) 3 and defective [C(NH 2 ) 3 ]Fe 2/3 III □ 1/3 (HCOO) 3 , and establish how missingion vacancies control the structural response to pressure and temperature variation in molecular perovskites for the first time. Upon compression, defects selectively soften the average strut length r ̅ , without having an effect on the hinging angle θ. The defective GuaFe 2/3 □ 1/3 undergoes a thermal phase transition not observed in GuaMn, yet both systems exhibit similar thermal expansion behavior. Placing our results in the context of efforts to manipulate the free energy landscape in coordination polymers, we stress that using defects as a tool to access (stimuli-responsive) properties is an increasingly appealing strategy. For instance, barocaloric behavior has recently been observed in certain molecular perovskites 54 and defects offer intriguing opportunities for controlling the underlying thermodynamics to optimize the barocaloric performance. In particular, defects flatten the underlying free energy surface, which is expected to impact phase transition temperatures. This suggests that defects can be used to enhance the barocaloric properties, for example, by optimizing the temperature of the barocaloric phase transition. More broadly, it will be exciting to see how defects will be exploited to learn about the fundamental interactions in coordination networks. The bulk modulus appears to be an important probe for the impact of defects on the underlying chemical interactions as reflected in the free energy landscape.
Experimental details, XRD patterns, evolution of lattice parameters as a function of temperature and pressure, and f−F plots (PDF)